Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x - 4} = \dfrac{-2x + 24}{x - 4}$
Explanation: Multiply both sides by $x - 4$ $ \dfrac{x^2}{x - 4} (x - 4) = \dfrac{-2x + 24}{x - 4} (x - 4)$ $ x^2 = -2x + 24$ Subtract $-2x + 24$ from both sides: $ x^2 - (-2x + 24) = -2x + 24 - (-2x + 24)$ $ x^2 + 2x - 24 = 0$ Factor the expression: $ (x - 4)(x + 6) = 0$ Therefore $x = 4$ or $x = -6$ However, the original expression is undefined when $x = 4$. Therefore, the only solution is $x = -6$.